I've been using inspin lately and so has Nick Woolsey... but I'm not entirely happy with it.
*technical blather warning*
I'd like to get a handle on what everyone thinks of as compound circles/flowers, antispin and "inspin", along with trammels/ various 1:1 patterns.
I like to model things in my mind (and 3ds max) from an external observer's point of view (say a camera on a tripod) rather than a 1st person view of what your wrist is having to do. This allows focus on the geometric relations, and you figure out how your body is supposed to do that. I also like to pay attention to "phase":
the orientation of the staff at the beginning of the pattern's cycle. Usually I find 4 possible phases are adequate to use: Horizontal or vertical, with staff ends A-B or B-A. I'll describe things from this point of view:
You have a static spin, where your hand stays at a point but the staff rotates.
You have R-types/flats or whatever they are called:
The hand/center of staff makes a circle, but the staff stays vertical or horizontal. This is a 1:0 ratio of hand orbit to staff rotating, but each head does still make a circular orbit... so in terms of circular orbits, is it a ratio of 1:1?!
Linear hand movements:
Move your hand in a line wile you spin and you get variations on a cycloid.
You have things in the Trammel/1:1 family:
There are plenty of these beyond the one where end A makes a line, the center makes a perpendicular line, and end B makes an ellipse.
I consider a 1:1 staff antispin a form of trammel. Some of these patterns have circular hand paths, some have ellipses, some have linear hand paths, but it's all a ratio of 1 hand cycle to 1 staff rotation. Some of these have an antispin quality to them, some don't. Staff isolations, extensions, and "rockets" (90 off phase with a staff iso) are all 1:1 as well.
Then we have compound circles:
This is like a spirograph: The hand cycles on a circular path at a different rate than the staff is rotating.
So, you have a set of patterns where the staff is rotating slower than the hand cycle. This can happen in "anti-spin" or "in-spin". I've seen these referred to as super-anti-spin and super-spin. Can anyone clarify this? Does the "super" indicate the faster-than-staff hand speed?
Then you have the set of staff-rotating-faster than hand cycle. This can of course be "anti-spin" or "in-spin".
So it seems to me that "anti-spin" and "in-spin" are attributes that aren't necessarily synonymous with "flowers" or compound circles alone.
Further, you can take linear hand movements and assemble them together to form polygon hand paths and complex geometric hand paths, ala Cyrille and Zan. If they are closed paths, that your hand s repeatedly cycle, they have a path directionality, so can these be described as "anti-spin" or "in-spin", even though they can have moments that look like both?
Also, when you fold your staff from point to point, or both heads trace the same polygon, your hand path is actually "asteroid"-like, ie a star of N points made of N equal arcs of a circle, then flipped inside out. If we look at the entire hand path then we would say the former has a quality of "anti-spin", wile the latter a quality of "in-spin"... but if you look at only one arc, for that moment the staff is doing the recipricol, ie "folding anti-spin" is made up of fractions of point isolation, or "polygon tracing" is made up of fractions of "anti-spin".
In summation, good luck on naming this shiz in an accurate, meaningful, yet not-to-wordy way!!